i cant seem to figure this out
What is m^3 – 3m^2 = 5m – 15 factored?
It's interesting that the problem was posed this way because you might notice that you can use the Distributive Property on both sides:
m^2(m – 3) = 5(m – 3)
At this point you might decide to say "If m ≠ 3 then I can divide both sides by (m–3) to get m^2 = 5, where m = ±√(5) are the only two answers."
However, if instead you subtracted 5(m – 3) from both sides:
m^2(m – 3) – 5(m – 3) = 0
and used the Distributive Property:
(m – 3)(m^2 – 5) = 0
Substitute (√(5))^2 for 5:
(m – 3)(m^2 – (√(5))^2) = 0
Use Difference of Squares:
(m – 3)(m + √(5))(m – √(5)) = 0
That's the answer to, "What is m^3 – 3m^2 = 5m – 15 factored?"
But now, using the Zero Product Property, you can find the values of m that make it true:
(m – 3) = 0 ==> m = 3
(m – √(5)) = 0 ==> m = + √(5)
(m + √(5)) = 0 ==> m = – √(5)